A Reflection: Base Blocks Addition and IXL

Description

The lesson in review was designed for third grade students participating in an after school program.  Students selected for the program demonstrated need for intervention in the areas of both mathematics and literacy.  The program coordinator admitted students to the program based on reading level and GMADE scores.  Homogeneous student groups consisted of up to twelve students who attend four forty-five minute sessions divided between two days.  The intended standards addressed in the lesson from the MA Curriculum Framework included: 

·         “Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.” (P.42)

·         Fluently add within 1000 using strategies and algorithms based on place value.” (P.46)

The lesson design incorporated the use of two specific technology programs.  The Base Blocks Addition applet intended to allow students a visual representation of the addition process.  The applet selected provided a picture explaining commonly used terminology such as carrying to the next place value.  The second program, IXL, offered students an opportunity to apply the addition process illustrated with the Base Blocks Addition applet.  Additionally, IXL collected data on student performance recording the amount of time spent working on problems, the number of problems answered both correctly and incorrectly, and student responses to specific questions.  The lesson plan allotted time for whole-group and individual time to demonstrate and investigate the Base Block Addition applet.  Students used IXL individually and the data collected by the program used to assess student understanding of the indicated standards.  No changes were made to the original lesson plan prior to implementation.

Narrative

The initial two student groups who participated in the lesson described above comprised students with the lowest reading level and GMADE scores of all the student groups.  The lesson and objectives were introduced to the group using the SMART Board to demonstrate the applet and discuss place value and addition strategies using place value.  Students expressed interest in the applet and all wanted an opportunity to use the manipulative on the SMART Board.  Students were selected throughout the demonstration of how the applet worked to both explain the next step in the process and perform the described step using the SMART Board.  After seeing student interest in using the applet with the SMART Board, the decision to modify the original plan was made.  Instead of sending students to individual computers to investigate the Base Blocks Addition applet, the group remained together taking turns explaining steps of the addition process and using the manipulative.  After modeling the features of the applet and students collectively demonstrating how to use the applet to model and solve addition problems, students proceeded to individual computers and began applying the strategies for solving addition problems.  Allocating more time for the introduction of the applet as a whole group, the lesson ended with student work on IXL.  The closing discussion described in the original lesson plan was rescheduled to begin the next lesson before allowing additional time for students to complete problems using IXL.

Reflection

The intended objectives for the lesson included:  modeling numbers with three digits using base blocks, modeling and solving addition problems with numbers up to three digits, and explaining how place value can be used to solve addition problems.  Underlying assumptions about knowledge involved connecting representations to help develop concepts.  Affordances and constraints of the knowledge presented are discussed in conjunction with the benefits and drawbacks of selected technologies in a following paragraph.  The planned demonstrations of both Base Blocks Addition and IXL represented information processing.  Although student led, the group discussion falls into the information processing category.  Constructivism was evidenced as students investigated the Base Blocks Addition applet individually and figured out how to use the tool to solve addition problems.  

The lesson designed was used as an intervention for low-achieving students.  The lesson’s objectives and goals align with those specified in the curriculum for third grade mathematics.  Student differences in learning were addressed offering the option of using the Base Blocks Addition manipulative to solve problems.  IXL also differentiates difficulty level by increasing difficulty as students correctly solve problems.  The virtual manipulative also addressed differences in learning styles by including numeric and visual representations.  The significance of the tool remains in that the applet highlights the connection between the numeric and visual representation offering insight into the addition process.

The class discussion provides an opportunity for instructors to gauge student understanding of place value and the process of adding numbers with up to three digits in addition to the feedback individualized IXL reports offer.  To be successful, IXL reports would demonstrate increased progress toward mastering the skill and students could explain mathematical ideas such as grouping, carrying, and decomposing numbers.

The technology identified for the lesson on addition of two numbers up to three digits served a variety of purposes.  First, the virtual manipulative played a critical role in helping students develop an understanding of the addition process by connecting common numeric representations with a visual representation.  The visual representation additionally offered students an image to refer to when explaining or discussing addition problems.  The applet communicated the content visually for students and allowed student manipulation of the blocks, both of which an advantage.  One disadvantage of the applet related to grouping or decomposing blocks.  Students were intrigued by this feature of the applet yet the feature remains limited.  For example, students wanted to move a block from the thousands place to the ones place; the applet only decomposed blocks one place-value lower.  The design of the blocks which represented specific place values were also advantageous for helping define each place value.  Many students referred to blocks in the tens column as “longs.”  When asked how long those blocks were, students could count the unit block markings to help develop an understanding of place-value name meanings. 

Second, IXL offered a platform for students to apply the strategies using grouping for addition problems as well as an assessment tool for the instructor.  Affordances of IXL included individualized problem sets which progress in difficulty based on student performance.  Additionally, the program provided a variety of reports for analysis of student progress indicating information such as incorrect responses and mastery of skills.  One drawback of coupling the Base Blocks Addition applet and IXL involved the reporting feature.  Creating and solving the given problem with the applet increased the amount of time taken on each problem.  IXL uses length of time to solve a problem as an indicator of student progress toward mastering a skill.  Looking forward, the Base Block Addition applet may be better used early on in presenting grouping strategies for addition and encouraging students to rely less on the tool as their understanding develops.  

The lesson also included other technologies such as the internet and SMART Board.  The SMART Board enabled an interactive demonstration of the applet’s features and the internet integral with the use of web-based technologies; however, the applet could have been demonstrated without the SMART Board.  Both SMART Board and internet were technologies used as a medium to access the applet and IXL but were not intended to significantly impact learning.  The most unique and significant contribution of the selected technologies remained the connections between numeric and visual representations for modeling addition.  

Students were excited to use the Base Blocks Addition applet.  The applet helped facilitate a whole-group discussion about place value and the addition process.  Student questions predominantly hinged upon features of the applet.  For the student who wanted to decompose the thousand-block, I asked how many blocks would be in each of the remaining columns to redirect and help connect how many groups of ones, tens, and hundreds make a thousand.

Digital Storytelling: Learning to Share

Understanding Student Understanding

Here's a link to an audio file of a student interview.  The student was asked to define a function.

 Student Interview: What is a Function?

Wicked Problem: Using Algebra Balance Scales Virtual Manipulative

Educational Need

Solving algebraic equations represents the focus of the educational need addressed with this project. More specifically, this project targeted the following two algebra standards:

• Understand that adding or subtracting the same number to both sides of an equation creates a new equation that has the same solution (A.FO.06.12)
• Understand that multiplying or dividing both sides of an equation by the same non-zero number creates a new equation that has the same solution (A.FO.06.13)

Proposed Technological Solution

After time spent both thinking and searching for strategies to teach solving equations, the decision was made to use the National Library of Virtual Manipulatives Algebra Balance Scales applet to address the educational need identified. The free Algebra Balance Scales applet provides students with a linked visual and symbolic representation of the equation which change concurrently once students modeled the equation and begin to solve to determine the value of the variable. As students selected an operation to perform to both sides, the changes are evidenced in both the equation as well as the blocks removed from the respective sides of the scale.

Technological Pedagogical Knowledge 

The selected technology, Algebra Balance Scales virtual manipulative, supports the teaching methods and strategies intended for the intervention. The applet scaffolds solving equations, models steps to solve an equation sequentially both symbolically and visually, and provided immediate feedback both verbally and visually to student responses. The applet offered students the opportunity to compare the created model and the given equation before proceeding to solving. Additionally, the virtual manipulative allowed for connections and observations to be made regarding how changes effect all representations of the equation, an advantage over using a physical manipulative to investigate solving equations.

Technological Content Knowledge

“Meaning does not reside in tools; it is constructed by students as they use tools.” Herbert and Colleagues (1997) quoted by Suh in Third Graders' Mathematics Achievement and Representation Preference Using Virtual and Physical Manipulatives for Adding Fractions and Balancing Equations. The Algebra Balance Scales applet helps make the content accessible by providing linked, multiple representations. The visual representation of the scale and blocks helps address student misconceptions regarding coefficients. The picture links to the symbolic representation by clarifying what coefficients actually mean. “One,” is a common response from students when given an equation such as 3x+7=13 and asked how many “x's” are on the left side. The manipulative helps address this misconception by providing verbal and visual feedback during the modeling phase. Students have the opportunity to recall prior information, or experience for the first time, that multiplication is repeated addition. Simultaneous manipulation of the scale and symbolic representation contribute greatly to the applet's support of the content and increased accessibility to students. The manipulative prompts students to work between both the visual and symbolic representation. As one representation is changed, students evidence how the change effected the other representation supports the learning objectives. Students watch as blocks are added, taken away, multiplied, or divided and the scale remains balanced. The differences in the two images demonstrate the linked representations previously described. The applet provides students an image of the intended learning goals.

Pedagogical Content Knowledge

The instructional strategies used for this intervention activity support the content much like the selected technology supports both content and pedagogy. Students ability to solve equations depends largely on a developed understanding of the symbolic representation. The misconception regarding coefficients discussed previously relates to the essential understanding of symbolic representations. Scaffolding supports the content by ensuring students have appropriately modeled the given equation. The scaffolding continues after the modeling phase also. This links to the importance and understanding of order of operations. Immediate feedback then continues the support of the content. Students proceed through the scaffold to solve the equation with appropriate mathematical moves; however, the feedback redirects students with a little hint to reconsider and manipulate the equation differently. Both symbolic and visual representations of equations further support the content's accessibility to students. As noted previously, verbal and visual feedback helps connect and develop an understanding of what manipulating an equation actually does to the equation. Again, the visual feedback contributes and supports the learning objectives by showing a balanced scale emphasizing the equality of both sides of the equation. Scaffolding, providing feedback and multiple representations, along with student manipulation of the applet all assist in making the content more accessible to students. 

Click here to read the full script.

Group Leadership Project: Jing Tutorial

Our group selected Screencast-O-Matic to capture demonstrating and narrating the features of Jing.  Using the screencast allowed for the viewer to actually see what the process will look like as the different steps and features were modeled and described.  With several unsuccessful attempts combining both the narration and visual models, I decided to capture the video and audio separately using Camtasia Studio.  Audacity was used to clean up the narration using the "noise removal" feature.  The video published above was produced using Camtasia to edit together the screencast and narration.  This allowed for smoother transitions, mistakes that were edited out, and a more professional representation of what Jing offers.

Working on this tutorial reaffirmed that the content, in many respects, is just as important as the delivery and modeling of the information.  Creating tutorials requires much the same thought process as lesson planning.  The audience must be considered.  Before creating the final product, it needs to be determined who the tutorial is intended for and the previous knowledge and experiences with technology anticipated.  Revisiting our tutorial, our group anticipated viewers to be familiar with computers and accessing the internet to download files as our tutorial began by encouraging viewers to download Jing.  Thinking through the development of the tutorial labeling these types of experiences as professional learning seems more fitting as considerations similar to those used in lesson planning occurred.  

In the future, I would be intentional about thinking through the tutorial itself as a professional learning experience.  Camtasia Studio offers different features which I would also include in the tutorial such as quizzing.  This would provide the viewer with a way to quickly self assess personal progress and understanding.  Additionally, I would consider captioning the tutorial to make it accessible to a greater population of people.  

Professional Learning Plan

Status Report:  In Progress.

Mobile Learning

The images presented above represent the poll created for my students. I experimented with the software and created both multiple choice and free response questions. Due to the approaching end of school, after the creation of the polls for students I printed and distributed the questions for students to respond to on their own. The software allows for polls to be left open. I left all three polls opened so students can submit their responses on their own time. The software allows polls to remain open for 30 days before the poll is automatically closed. Responses can be viewed as submitted allowing viewers to see the collected data immediately.


Joining the cell phones in education on Classroom 2.0, I found several posts sharing information regarding use of cell phones as well as questions other educators posed requesting feedback and advice about incorporating cell phones into the curriculum. I responded with some suggestions I had heard at a conference regarding appropriate use of cell phones in the classroom. One suggestion I had heard at the conference was to have students leave the phone on the desk until the time came to text a response. It provides a quick visual reference for the teacher to see which phones are or are not on the desk and in turn then further inquire as to what the cell phone is being used for.


In the past I've used laptops in the classroom.  The high school I taught at used Carnegie Learning Algebra which had an online software component.  Students used the laptops to complete instructional units using the software.  In addition, students used Gizmos; students completed the online simulations and then submitted work through e-mail.  My STEM geometry students were issued a flash drives for saving and storing their work.  Each student kept work on the drive so they could access it when needed.  The main issue that arose from using these drives were students forgetting to bring them or losing them. 


Mobile technology in the classroom offers many benefits.  Cell phones and iPods seem the most prevalent technologies in the hands of my students.  This seems a good place to start requiring some thought related to students participating without either technology.  I prefer the thought of cloud computing to USB or flash drives.  Work saved in a web-based program can be accessed anywhere with the internet regardless of the software installed on the computer being used.  It also helps eliminate the issue of lost drives.  Although interest in working with other technologies such as iPads or personal technology, the expense would need to be overcome.  I've heard of iPads being used in small groups to present projects to groups.  This would minimize the number necessary.  Ultimately, I'd like to incorporate mobile technology in my classroom as a method of participation for students such as cell phone polls.